Page 162 - Fluid-Structure Interactions Slender Structure and Axial Flow (Volume 1)

144 SLENDER STRUCTURES AND AXIAL FLOW

5 I I I I I

4

3

0
-30 -20 -10 0

15 I I I I I

-
10
3
a
5-

-30 -20 -10 0
Y
Figure 3.51 Comparison between theoretical and experimental values of u for (i) the threshold of
restabilization of pipes buckled under their own weight and (ii) onset of flutter of ‘standing’ vertical
cantilevers conveying air (p = 1.1 x lop3): 0, e, experiment; -, theory (PaYdoussis 1970).

approximately were not feasible, as the system then remained unstable at all flows; the
transition from instability by divergence to instability involving both divergence and
flutter proved to be very difficult to pin-point. It is also noted that the theoretical results
in Figure 3.51 are quite different, for the given B and p, from those in Figure 3.33 for
= O+, p = 0 - for the reasons discussed at the end of Section 3.5.3.
It is seen in Figure 3.51 that agreement between experiment and theory is quite good,
particularly in the case of the dimensionless flow velocities, where in most cases the
discrepancy is < 5%, which is within the margin of experimental error. It is also remarked
that, in this particular case, linear theory can predict the restabilization and second loss
of stability of an initially unstable system quite well.+
~~
+Provided that the system is first supported in more or less its equilibrium configuration and then released.